The precise roles played by the mock theta functions within the theory of modular forms remained unclear in the decades following Ramanujan's death shortly after he wrote his last letter to Hardy. However, the importance of these functions was clear – they have been shown to play meaningful roles in the diverse subjects of combinatorics, \(q\) -hypergeometric series, mathematical physics, elliptic curves and traces of singular moduli, Moonshine and representation theory, and more. Within the last 20 years we have also finally understood, with thanks to key work by Zwegers, Bruinier-Funke, and others including Bringmann-Ono and Zagier [1]}, that the mock theta functions turn out to be examples of mock modular forms, which are holomorphic parts of harmonic Maass forms, modern relatives to ordinary Maass forms and modular forms. This context has also allowed us to make more sense of the notion of the order of a mock theta function. For more background and information on these aspects of the mock theta functions, see, e.g., [1]}, [3]}, [4]}, [5]}.
